Preheat large, heavy skillet over medium high heat.
Set steaks on to a waxed paper lined work surface and cover with another piece of waxed paper. Pound steaks to 1/4-inch thick. Pull steaks off work surface and set to the side. Line work surface with more waxed paper. Pour 1/2 cup flour into 2 piles on opposite sides of the work space. Add cornmeal, paprika, salt and pepper to 1 pile of flour. Beat eggs and water in a pie plate or shallow dish.
Cut steaks into 4 portions and coat in flour, eggs, then seasoned flour and cornmeal.
Add 2 tablespoons oil to hot pan and cook 2 steaks at a time. Brown steaks about 2 minutes per side, or until cooked and remove from the pan. Add 2 tablespoons more oil and repeat with remaining 2 steaks. Remove steaks to serving platter and pour off all but 2 to 3 tablespoons of drippings. Add 2 tablespoons flour to drippings and cook 2 minutes. Whisk in broth and season with salt and pepper. Whisk half and half or cream into gravy. When gravy bubbles, remove from heat.